Tag: machine learning

How is Calculus Used in Computer Science

The Multifaceted Influence of Calculus in Computer Science: From Graphics and Animation to Signal Processing and Computational Physics

Calculus, an indispensable mathematical tool, fuels innovation and advancements in computer science. Its versatility spans across multiple domains, including graphics and animation, signal processing and image analysis, as well as computational physics and engineering. In this article, we explore how calculus shapes computer science, from optimizing algorithms and navigating differentiable manifolds to enabling lifelike graphics, precise signal processing, and accurate simulations. Let’s dive into the multifaceted influence of calculus in the world of computer science.

Optimization and Numerical Analysis: Unleashing Algorithmic Efficiency

Calculus techniques, including differentiation and integration, play a crucial role in optimizing algorithms and conducting numerical analysis. Methods like gradient descent leverage calculus to adjust algorithm parameters, enhancing their performance and convergence. Numerical analysis, empowered by calculus, enables the efficient solving of complex equations, simulations of physical systems, and processing of extensive datasets. These applications contribute to enhanced computational efficiency and improved problem-solving capabilities in computer science.

Machine Learning and Differentiable Manifolds: The Power of Gradients

Machine learning, a thriving field of computer science, relies heavily on calculus for model optimization and training. Techniques such as backpropagation and gradient descent employ calculus to adjust weights and minimize errors in neural networks. Furthermore, differentiable manifolds provide a geometric framework for understanding complex data spaces. By leveraging calculus on these manifolds, computer scientists gain insights into data patterns, clustering, and geometric modeling, leading to breakthroughs in pattern recognition, data analysis, and computer-aided design.

Graphics and Animation: Bringing Virtual Worlds to Life

Calculus serves as the backbone for creating captivating graphics and lifelike animations. Concepts such as vectors, matrices, and parametric equations enable computer scientists to model and manipulate 3D objects and their motion. Calculus facilitates the rendering of smooth animations, realistic lighting effects, and physics-based simulations. Through the integration of calculus, computer-generated graphics and animations are able to immerse users in visually stunning virtual environments.

Signal Processing and Image Analysis: Unveiling Insights from Data

In signal processing and image analysis, calculus provides essential tools for extracting meaningful information from raw data. Techniques like Fourier analysis, wavelet transforms, and convolution employ integral calculus to analyze and process signals, images, and videos. Calculus-based operations enhance images, detect patterns, remove noise, and compress data efficiently. These applications find wide use in fields such as image recognition, medical imaging, video processing, and audio analysis.

Computational Physics and Engineering: Simulating Real-World Phenomena

Calculus is instrumental in computational physics and engineering simulations. It enables scientists and engineers to model complex physical systems, simulate fluid dynamics, and solve differential equations that govern these phenomena. By converting continuous equations into numerical approximations, calculus allows for precise simulations and predictions of real-world behavior. From exploring the behavior of celestial bodies to designing efficient structures, calculus empowers computer scientists to tackle complex problems and drive advancements in diverse fields.

Conclusion

Calculus is an essential force driving innovation in computer science. Its diverse applications extend beyond optimization and numerical analysis, permeating domains such as graphics and animation, signal processing and image analysis, as well as computational physics and engineering. By harnessing the power of calculus, computer scientists can optimize algorithms, navigate differentiable manifolds, and unlock transformative applications in lifelike graphics, precise signal processing, and accurate simulations. As the integration of calculus and computer science progresses, we can anticipate a future marked by stunning virtual environments, intelligent data analysis systems, and precise simulations of the natural world.

Math Books for Machine Learning

📚 Best Books for Machine Learning Mathematics 🧠

Are you ready to embark on an exhilarating journey into the world of machine learning? To truly master this cutting-edge field, you need a solid foundation in mathematics—the language of algorithms and data analysis. Whether you’re a beginner or an experienced data enthusiast, we’ve handpicked a selection of math books that will catapult your machine learning prowess to unprecedented heights! Get ready to dive deep into the numerical realm and elevate your skills to the next level. 🚀

📖 Book 1: “Mathematics for Machine Learning” by Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong 📖

Mathematics for Machine Learning

This gem of a book is an absolute must-have for anyone venturing into the realm of machine learning. Seamlessly blending theory and practice, the authors deliver a comprehensive guide to the mathematical foundations essential for success in this field. From linear algebra to calculus and optimization techniques, you’ll gain a profound understanding of the mathematical tools that power machine learning algorithms. This indispensable resource is filled with intuitive explanations, real-world examples, and interactive exercises, ensuring your journey from mathematical novice to machine learning maven is both enlightening and enjoyable!

📖 Book 2: “Pattern Recognition and Machine Learning” by Christopher M. Bishop 📖

Pattern Recognition and Machine Learning (Information Science and Statistics)

Prepare to be captivated by this masterpiece that beautifully marries pattern recognition and machine learning. Bishop’s expertise shines through every chapter as he navigates you through the intricate landscape of statistical inference and probabilistic modeling. With an emphasis on understanding mathematical concepts from a practical standpoint, this book equips you with the skills to tackle complex machine learning challenges head-on. With its accessible writing style, comprehensive coverage, and hands-on exercises, “Pattern Recognition and Machine Learning” will become your trusted companion on your journey to becoming a machine learning maestro!

📖 Book 3: “Deep Learning” by Ian Goodfellow, Yoshua Bengio, and Aaron Courville 📖

Deep Learning (Adaptive Computation and Machine Learning series)

Take a deep breath and prepare to immerse yourself in the world of deep learning—a domain where mathematics meets artificial intelligence in the most extraordinary way. Goodfellow, Bengio, and Courville have created a masterpiece that will unlock the secrets of neural networks and convolutional architectures. By interweaving the theoretical underpinnings with practical insights, this book unravels the mysteries of deep learning, empowering you to build and train your own state-of-the-art models. Embark on an exhilarating journey where calculus, linear algebra, and probability theory converge to reshape the boundaries of what’s possible!

📖 Book 4: “The Elements of Statistical Learning” by Trevor Hastie, Robert Tibshirani, and Jerome Friedman 📖

The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition (Springer Series in Statistics)

Get ready to delve into the fascinating world of statistical learning—a discipline that underpins the very essence of machine learning. Hastie, Tibshirani, and Friedman provide an in-depth exploration of the statistical principles that drive cutting-edge algorithms. With a treasure trove of illustrative examples and thought-provoking exercises, this book guides you through the intricate tapestry of regression, classification, and clustering techniques. Equip yourself with the tools of the trade and unravel the hidden patterns that lie within vast data sets!

🔥 Harness the Power of Mathematics and Unleash Your Machine Learning Potential! 🔥

These four math books are the catalysts that will revolutionize your machine learning journey. By mastering the mathematical foundations, you’ll gain a competitive edge in this rapidly evolving field. Whether you’re a data scientist, a programmer, or an aspiring machine learning enthusiast, these books will become your trusted companions on the road to success.

Best Laptop for Deep Learning

Unleash Your Deep Learning Potential with the Best Laptop: Power up Your Machine Learning Journey!

When it comes to deep learning, having the best laptop at your disposal is paramount. We have meticulously handpicked the top-rated laptops, specifically designed to meet the rigorous demands of machine learning computations. These laptops combine powerful processing capabilities, ample memory, cutting-edge graphics (GPUs), and lightning-fast speeds, making them the ultimate machines for deep learning enthusiasts. Say goodbye to bottlenecks and embrace the limitless possibilities of artificial intelligence with these extraordinary laptops.

Dell XPS 15: Experience Power and Portability

The Dell XPS 15 is a true workhorse for deep learning tasks. Powered by Intel Core processors and NVIDIA GeForce graphics, this laptop provides exceptional performance for demanding machine learning workloads. With options for dedicated GPUs like the NVIDIA GeForce GTX or RTX series, you’ll experience lightning-fast computations and smooth model training. Its stunning 4K OLED display brings visuals to life, enhancing your deep learning experience. Discover the Dell XPS 15 on Amazon and unleash your computational power.

Dell XPS 15 9500 (Latest Model) 15.6-inch Laptop

ASUS ROG Zephyrus G14: Mobility and Performance Combined

The ASUS ROG Zephyrus G14 offers a perfect balance of mobility and performance for deep learning enthusiasts on the go. Equipped with AMD Ryzen processors and NVIDIA GeForce RTX graphics, this laptop delivers outstanding performance for machine learning tasks. The inclusion of dedicated GPUs with CUDA cores ensures accelerated model training and efficient computations. Its compact design, long battery life, and efficient cooling system make it an excellent choice for deep learning on the move. Explore the ASUS ROG Zephyrus G14 on Amazon and revolutionize your machine learning journey.

EXCaliberPC 2022 ASUS ROG Zephyrus G14

Lenovo ThinkPad P15: Enterprise-Grade Powerhouse

For professionals and researchers requiring enterprise-grade performance, the Lenovo ThinkPad P15 is the ultimate deep learning powerhouse. With options for Intel Xeon processors and NVIDIA Quadro graphics, this laptop delivers unmatched computational capabilities. Its dedicated GPUs equipped with Tensor Cores enable lightning-fast training and inferencing for deep learning models. The ThinkPad P15’s exceptional build quality, expansive memory and storage options, and stunning display ensure a seamless deep learning experience. Unleash the capabilities of the Lenovo ThinkPad P15 on Amazon.

OEM Lenovo ThinkPad P15s 

Are Gaming Laptops Good for Machine Learning?

In general, yes, gaming laptops are good for machine learning and deep learning.

The main reason is due to the dedicated Graphics Processing Unit (GPU) on gaming laptops. Gaming laptops are typically equipped with powerful dedicated GPUs, such as NVIDIA GeForce RTX or GTX series. These GPUs come with CUDA cores that can greatly accelerate machine learning tasks, particularly for training deep neural networks. They provide parallel processing capabilities that significantly speed up model training times.

There is a huge range of gaming laptops on Amazon that are suitable for the dual purpose of deep learning and gaming. Choose one that has high RAM and a good GPU, and it will generally be suitable for deep learning and machine learning tasks.

Do note that for training very large machine learning models, there may still be a need to rent a more powerful GPU on the cloud. The laptop will still be useful though for the initial data cleaning, as well as testing out the deep learning training for a subset of the dataset.

Laptop for data science and machine learning

We recommend and review some laptops/notebooks suitable for data science and machine learning.

Firstly, we state the 4 core important specs (specifications) for laptops for data science and machine learning.

1) RAM: Should be 8GB or higher.

2) CPU: Should be Intel Core i5, or even better Intel Core i7.

3) Storage: Should be at least 256 GB SSD.

4) GPU: Optional, but good to have for deep learning. (Note that Mac GPUs are not usable for deep learning.)

RAM and CPU are necessary in order to conduct computations successfully and within a reasonable time. Storage is necessary to process big data which can potentially be several gigabytes. GPU is useful to speed up deep learning, but is optional since there are many cloud or server options available.

For concrete recommendations, we recommend the following 5 laptops. Certainly, there could be other laptops that are equally suitable for data science and machine learning, do comment below if you have a good suggestion!

1)

ASUS ROG Strix Scar 17 Gaming Laptop, 17.3” 300Hz FHD IPS Type, NVIDIA GeForce RTX 2070 Super, Intel Core i7-10875H, 16GB DDR4, 1TB PCIe SSD, Per-Key RGB Keyboard, Wi-Fi 6, Windows 10, G732LWS-DS76

2)

Dell XPS 15 7590 Laptop 15.6 inch, 4K UHD OLED InfinityEdge, 9th Gen Intel Core i7-9750H, NVIDIA GeForce GTX 1650 4GB GDDR5, 256GB SSD, 16GB RAM, Windows 10 Home, XPS7590-7572SLV-PUS, 15-15.99 inches

3)
New Apple MacBook Pro (16-inch, 16GB RAM, 512GB Storage, 2.6GHz Intel Core i7) – Space Gray

4)

2020 Lenovo ThinkPad T590 15.6″ FHD Full HD (1920×1080) Business Laptop (Intel Quad-Core i7-8565U, 16GB RAM, 512GB SSD) Backlit, Type-C Thunderbolt 3, RJ-45, Webcam, Windows 10 Pro IST Computers

5)
HP Pavilion 15-inch Laptop, Intel Core i7, 16 GB RAM, 512 GB SSD Storage, Intel Iris Plus Graphics, Windows 10 Pro, Amazon Alexa Voice Compatible (15-cs3019nr, Mineral Silver)

Updating Spyder takes forever

Spyder is a Python IDE that is bundled together with the Anaconda distribution.

There are some problems that are commonly faced when it comes to updating Spyder. One way to update Spyder is to open Anaconda Navigator and click the settings button which has an option to update Spyder. But the problem is that the process can take a very long time. The process shows that it is “loading packages of /User/…/opt/anaconda3”.

Updating Spyder is constricted by …

Another way to update Spyder is to type “conda update spyder” in the terminal. A problem that can crop up is the error message: “updating spyder is constricted by …”

Anaconda stuck updating Spyder [Solved]

For my case, it turns out that the version of Anaconda Navigator is outdated. Hence, I first updated Anaconda Navigator to the latest version.

Then, instead of clicking “Update application” which still didn’t quite work, we click on “Install specific version” and choose the latest version of Spyder (Spyder 4.1.5 in this case).

Then, the updating of Spyder in Anaconda Navigator worked perfectly!

How to update Spyder using Anaconda-Navigator: Click “Install specific version” instead of “Update application”.

Best Udemy Data Science / Machine Learning / AI Courses

During this current lockdown period it is a good idea to pick up a data science skill. Most occupations can benefit from such a skill, including engineers, accountants, teachers, even students. Who knows, one day you may find deep learning useful!

In this page we introduce various Udemy courses (which come with certificates that you can put on your LinkedIn profile) that are the best in their class, be it for data science, machine learning (including deep learning), and AI (Artificial Intelligence).

Best Udemy Python Course

Currently, Python is the most popular language for data science and machine learning.  R is the second most popular language, and is especially good for statistics.

Hence, this Machine Learning A-Z™: Hands-On Python & R In Data Science Course is perfect as it introduces two of the most popular programming languages in one course! You will learn Machine Learning (ML) in the process as well, which is a great bonus.

If you only want to focus on Python, then check out 2020 Complete Python Bootcamp: From Zero to Hero in Python. It is designed to bring you from zero knowledge to a respectable expert in Python if you complete the course and exercises.

Best Udemy courses for data science

In the Python for Data Science and Machine Learning Bootcamp  course, students can learn how to use NumPy, Pandas, Seaborn, Matplotlib, Plotly, Scikit-Learn, Machine Learning, Tensorflow, and more! The aforementioned packages are all classic and popular in data science, data analysis and data visualization.

The Data Science Course 2020: Complete Data Science Bootcamp is another bootcamp style course that gives you complete Data Science training in: Mathematics, Statistics, Python, Advanced Statistics in Python, Machine & Deep Learning. It is especially suitable for beginners, as well as intermediate students who need to brush up on their skills.

Best Udemy course for Deep Learning

Deep learning (DL) is a subbranch of machine learning that is recently very hot and popular due to its superior accuracy in tasks such as image classification and NLP (natural language processing).

The Deep Learning A-Z™: Hands-On Artificial Neural Networks allows students to learn how to create Deep Learning Algorithms in Python from two Machine Learning & Data Science experts. Templates included, which is very important. Essentially, you can use and modify the templates to suit your individual task at hand.

Complete Guide to TensorFlow for Deep Learning with Python is a course for learn how to use Google’s Deep Learning Framework – TensorFlow with Python! Solve problems with cutting edge techniques! TensorFlow is one of the more popular deep learning framework, and is slightly ahead in popularity compared to its closest rival, PyTorch.

Udemy course benefits

The first benefit of Udemy courses, is that you get to learn content from the top trainers. Often, these courses are superior to free YouTube content, and may be even better than the courses in your school.

The second benefit is that Udemy provides a certificate upon completion that you can list in your CV, as well as put in your LinkedIn profile. This is especially important if you are trying to transition into a data scientist job from another field, like engineering or physical sciences.

What is your favorite Udemy course for AI/ML/DL? Feel free to comment below!

Best Pattern Recognition and Machine Learning Book (Bishop)


Pattern Recognition and Machine Learning (Information Science and Statistics)

The above book by Christopher M. Bishop is widely regarded as one of the most comprehensive books on Machine Learning. At over 700 pages, it has coverage of most machine learning and pattern recognition topics.

It is considered very rigorous for a machine learning (data science) book, but yet has a lighter touch than a pure mathematics or theoretical computer science book. Hence, it is perfect as a reference book or even textbook for students self learning the subject from the ground up (i.e. students who want to understand instead of just blindly apply algorithms).

A brief overview of the contents covered (taken from the contents page of the book):

  1. Introduction

  2. Probability Distributions

  3. Linear Models for Regression

  4. Linear Models for Classification

  5. Neural Networks

  6. Kernel Methods

  7. Sparse Kernel Machines

  8. Graphical Models

  9. Mixture Models and EM

  10. Approximate Inference

  11. Sampling Methods

  12. Continuous Latent Variables

  13. Sequential Data

  14. Combining Models

Python save csv to folder

In Python (pandas), saving a .csv file to a particular folder is not that hard, but then it may be confusing to beginners.

The packages we need to import are:

import pandas as pd
import os.path

Say, your folder name is called “myfolder”, and the dataframe you have is called “df”. To save it insider “myfolder” as “yourfilename.csv”, the following code does the job:

df.to_csv(os.path.join('myfolder','yourfilename.csv'))

The reason this may be difficult for beginners is that beginners may not know of the existence of the os.path.join method, which is the recommended method for joining one or more path components.

Recall & Precision vs Sensitivity & Specificity

Other than accuracy rate, there are various metrics for machine learning to measure how “accurate” the model is.

Some popular ones for binary classification are sensitivity (true positive rate) and specificity (true negative rate).

In computer science, recall and precision are also common metrics.

It can be quite confusing to remember offhand what each metric means, and how they are related.

To summarize, the following are equivalent (for binary classification):

sensitivity = recall of positive class

specificity = recall of negative class

Sample source: https://onlinelibrary.wiley.com/doi/pdf/10.1002/cmdc.201700180

Other than the above metrics mentioned, there are also many other metrics, such as F1 score, etc.

pip install keeps installing old/outdated packages

This article is suitable for solving the following few problems:

  1. module ‘sklearn.tree’ has no attribute ‘plot_tree’
  2. pip install (on Spyder, Anaconda Prompt, etc.) does not install the latest package.

The leading reason for “module ‘sklearn.tree’ has no attribute ‘plot_tree” is because the sklearn package is outdated.

Sometimes “pip install scikit-learn” simply does not update the sklearn package to the latest version. Type “print(sklearn.__version__)” to get the version of sklearn on your machine, it should be at least 0.21.

The solution is to force pip to install the latest package:

pip install --no-cache-dir --upgrade <package>

In this case, we would replace <package>  by “scikit-learn”.

Sometimes, pip install does not work in the Spyder IPython console, it displays an error to the effect that you should install “outside the IPython console”. This is not normal (i.e. it should not happen), but as a quick fix you can try “pip install” in Anaconda Prompt instead. It is likely that something wrong went on during the installation of Anaconda, Python, and the long-term solution is to reinstall Anaconda.

caret package in R: known issue when converting factor variables

In the R language, often you have to convert variables to “factor” or “categorical”. There is a known issue in the ‘caret’ library that may cause errors when you do that in a certain way.

The correct way to convert variables to ‘factor’ is:

trainset$Churn = as.factor(trainset$Churn)

In particular, “the train() function in caret does not handle factor variables well” when you convert to factors using other methods.
(See https://rpubs.com/SulmanKhan/444033)

Basically, if you use other ways to convert to ‘factor’, the code may still run, but there may be some ‘weird’ issues that leads to inaccurate predictions (for instance if you are doing logistic regression, decision trees, etc.)

How to save sklearn tree plot as file (Vector Graphics)

The Scikit-Learn (sklearn) Python package has a nice function sklearn.tree.plot_tree to plot (decision) trees. The documentation is found here.

However, the default plot just by using the command

tree.plot_tree(clf)

could be low resolution if you try to save it from a IDE like Spyder.

The solution is to first import matplotlib.pyplot:

import matplotlib.pyplot as plt

Then, the following code will allow you to save the sklearn tree as .eps (or you could change the format accordingly):

plt.figure()
tree.plot_tree(clf,filled=True)  
plt.savefig('tree.eps',format='eps',bbox_inches = "tight")

To elaborate, clf is your Decision Tree classifier (to be defined before plotting the tree):

# Example from https://scikit-learn.org/stable/modules/generated/sklearn.tree.plot_tree.html
clf = tree.DecisionTreeClassifier(random_state=0)
clf = clf.fit(iris.data, iris.target)

The outcome is a Vector Graphics format (.eps) tree that will retain its full resolution when zoomed in. The bbox_inches=”tight” command prevents truncating of the image. Without that command, sometimes the sklearn tree will just be cropped off and be incomplete.

Introduction to Machine Learning

Very good introduction to Machine Learning by Google. Google is the developer of Tensorflow (on which the Keras package is built). The other platform for Machine Learning is Pytorch by Facebook.

So far, the best introductory book to Machine Learning seems to be the one by the founder of Keras, called “Deep Learning with Python”. See also Best Machine Learning / Deep Learning Books.